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Modular tensor category
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<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, a modular tensor category is a type of <a href="/facts/Tensor_category/F2l5oKMD">tensor category</a> that plays a role in the areas of <a href="/facts/Topological_quantum_field_theory/zHjrp3b8">topological quantum field theory</a>, <a href="/facts/Conformal_field_theory/McVlk4hR">conformal field theory</a>, and <a href="/facts/Quantum_algebra/yaRQuM8P">quantum algebra</a>. Modular tensor categories were introduced in 1989 by the physicists <a href="/facts/Greg_Moore_(physicist)/7WCVjHHt">Greg Moore</a> and <a href="/facts/Nathan_Seiberg/fXv7kvGs">Nathan Seiberg</a> in the context of <a href="/facts/Rational_conformal_field_theory/0zPsDp63">rational conformal field theory</a>. In the context of <a href="/facts/Quantum_field_theory/VoewsNJV">quantum field theory</a>, modular tensor categories are used to store algebraic data for <a href="/facts/Rational_conformal_field_theory/0zPsDp63">rational conformal field theories</a> in (1+1) dimensional spacetime, and <a href="/facts/Topological_quantum_field_theory/zHjrp3b8">topological quantum field theories</a> in (2+1) dimensional spacetime. In the context of <a href="/facts/Condensed_matter_physics/EBVI5nmL">condensed matter physics</a>, modular tensor categories play a role in the algebraic theory of topological quantum information, as they are used to store the algebraic data describing <a href="/facts/Anyons/hfgpCFjf">anyons</a> in <a href="/facts/Topological_order/EfEnKRSw">topological quantum phases of matter</a>. </p><p>Mathematically, a modular tensor category is a rigid, <a href="/facts/Semi-simplicity/Wz7E1GbT">semisimple</a>, braided fusion category with a non-degenerate braiding, ensuring a well-defined notion of topological <a href="/facts/Invariant_(mathematics)/9TeNN2ed">invariance</a>. These categories naturally arise in <a href="/facts/Quantum_group/huNTuaXs">quantum groups</a>, <a href="/facts/Representation_theory/3ydLtaGH">representation theory</a>, and <a href="/facts/Low-dimensional_topology/o5g9aRGw">low-dimensional topology</a>, where they are used to construct knot and three-<a href="/facts/Manifold_(mathematics)/rXPERJtu">manifold</a> invariants. </p>